Global Simulations of Astrophysical Jets in Poynting Flux

Dominated Regime

Hui Li

S. Colgate, J. Finn, G. Lapenta, S. Li

Engine; Injection; Collimation; Propagation; Stability; Lobe Formation; Dissipation; Magnetization of IGM

Leahy et al.1996

I. Engine and Injection

Approach: Global Configuration Evolution without modeling the accretion disk physics. Replace accretion disk with a “magnetic engine” which pumps flux (mostly toroidal) and energy.

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Flux fn. (cylin.) Ψ = r2 exp(−r2 − k 2z2)

B =

Br = 2k 2z r exp(−r2 − k 2z2)

Bz = 2(1− r2) exp(−r2 − k 2z2)

Bφ =f (Ψ)

r = α r exp(−r2 − k 2z2)

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

q(r) = krBzBφ

= 2k(1− r2)

α

Mimicking BH-Accretion System? : Initial poloidal fields on “disk”, exponential drop-offf() : B profile, or disk rotation profile : toroidal/poloidal flux ratioJxB : radial pinching and vertical expansionJpxBp: rotation in direction, carrying angular momentum?

=5

=0.1

=3

Li et al.’05

Problems:No disk dynamicsFootpoints allowed to move, though could be in equilibriumNot precisely KeplerianMass loading?Dipole or Quadrupole

Injection

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∂B

∂t= B(r,z) γ(t)

1) An initial state modeled as a magnetic spring (=3).2) Toroidal field is added as a function of time over a small central region:

3) Adding twists, self-consistently collimate and expand.

Impulsive Injection: Evolution of a highly wound and compressed magnetic “spring” Continuous Injection: Evolution of “magnetic tower” with continuous injected toroidal and/or poloidal fields

II. Collimation; Propagation

Run A: impulsive injection, =50 vinj >> vA > cs

Run B: continuous injection, =3, =3 vA > cs, scanning through (vinj)

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Run A

|B| at cross-section

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Run A

Total |B|

Current density

Run A Run A-2Kinetic KineticMagneti

cMagnetic

III. Stability and Lobe Formation

Dynamic: moving, q-profile changing

3D Kink unstable in part of helix: twist accumulation due to inertial/pressure confinement

Pressure profile: hollow

Velocity profile ?

radius

height

Pressure EvolutionIn Implusive

Injection Case

Azimuthally averaged

Poloidal Flux (n=0)

radius

height

3D Flux Conversion

Continuous Injection

radius

height

Azimuthally Averaged

Poloidal Flux

Run B: Continuous Injection

Injected toroidal flux vs time

Poloidal flux at disk surface

Z (height)

T=0

T=4 T=8 T=12

T=16

B flux

A Moving “Slinky”

T=0 T=3

T=5 T=10

pressure

height

HelixStability

radius

Lobe Formation

Continuous Injection

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∂B

∂t= Bφ(r,z) γ (t)

1) An initial state modeled as a magnetic spring (=3).2) Toroidal field is added as a function of time over a small central region:

3) Adding twists, self-consistently collimate and expand.

Time

B flux

Kink unstable

High Injection Rate

Kink unstable

Conclusion: Lessons Learned

Field lines must “lean” on external pressure, concentrating twists to the central region --- collimation.

a) Static limit:

Expansion is fast, reducing the toroidal field per unit height. Velocity difference between the base and the head causes the head to undergo 3D kink, forming a fat head --- lobes (?).

b) Impulsive injection limit:

c) Continuous injection: Non-uniform twist distribution along height. Map out the dependence on injection rates.

In all cases, external pressure plays an important “confining” role, helping collimation and stability.